Precalculus: Mathematics for Calculus, 7th Edition

by
Stewart, James; Redlin, Lothar; Watson, Saleem

Published by
Brooks Cole

ISBN 10:
1305071751

ISBN 13:
978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises: 79

Answer

$\left[ 2,8 \right]
$

Work Step by Step

For any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$. (The symbol $\lt$ may be replaced with $\le$.)
Using the concept above, the solutions to the given inequality, $
|x-5|\le3
,$ is
\begin{array}{l}\require{cancel}
-3\le x-5\le3
\\\\
-3+5\le x\le3+5
\\\\
2\le x\le8
.\end{array}
In interval notation, the solution set is $
\left[ 2,8 \right]
.$